As Eager Construct’s triggered ability resolves, first the player whose turn it is scrys 1, then each other player in turn order does the same. Each player will know the choices made by players who chose before them.

6/8/2018

If multiple players are instructed to scry at once, such as while resolving Eager Construct’s triggered ability, those players each look at the top card of their library at the same time, then they choose in turn order whether to put those cards on the top or bottom of their library.